In this vignette, we fit two variable selection models: the first (“null”) model has a uniform prior for all variables (the 442,001 genetic markers); the second model has higher prior probability for genetic markers near cytokine signaling genes. This analysis is intended to assess support for enrichment of Crohn’s disease risk factors near cytokine signaling genes; a large Bayes factor means greater support for this enrichment hypothesis. The data in this analysis consist of 442,001 SNPs genotyped for 1,748 cases and 2,938 controls. Note that file `cd.RData`

cannot be made publicly available due to data sharing restrictions, so this script is for viewing only.

Begin by loading a couple packages into the R environment.

```
library(lattice)
library(varbvs)
```

Set the random number generator seed.

`set.seed(1)`

```
load("cd.RData")
data(cytokine)
```

Here we compute the variational approximation given the assumption that all variables (genetic markers) are, *a priori*, equally likely to be included in the model.

`fit.null <- varbvs(X,NULL,y,"binomial",logodds = -4,n0 = 0)`

Next, compute the variational approximation given the assumption that genetic markers near cytokine signaling genes are more likely to be included in the model. For faster and more accurate computation of posterior probabilities, the variational parameters are initialized to the fitted values computed above with the exchangeable prior.

```
logodds <- matrix(-4,442001,13)
logodds[cytokine == 1,] <- matrix(-4 + seq(0,3,0.25),6711,13,byrow = TRUE)
fit.cytokine <- varbvs(X,NULL,y,"binomial",logodds = logodds,n0 = 0,
alpha = fit.null$alpha,mu = fit.null$mu,
eta = fit.null$eta,optimize.eta = TRUE)
```

Compute the Bayes factor.

`BF <- varbvsbf(fit.null,fit.cytokine)`

```
save(list = c("fit.null","fit.cytokine","map","cytokine","BF"),
file = "varbvs.demo.cytokine.RData")
```

Show two “genome-wide scans” from the multi-marker PIPs, with and without conditioning on enrichment of cytokine signaling genes.

```
i <- which(fit.null$pip > 0.5 | fit.cytokine$pip > 0.5)
var.labels <- paste0(round(map$pos[i]/1e6,digits = 2),"Mb")
print(plot(fit.null,groups = map$chr,vars = i,var.labels = NULL,
gap = 7500,ylab = "posterior prob."),
split = c(1,1,1,2),more = TRUE)
print(plot(fit.cytokine,groups = map$chr,vars = i,var.labels = var.labels,
gap = 7500,ylab = "posterior prob."),
split = c(1,2,1,2),more = FALSE)
```